(24,12) Golay code encoders and decoders based on the non-binary hexacode have been used in the communication systems for error handling. The family of hexacode-based Golay decoders is very valuable because of the low complexity involved in soft-decision decoding of the popular (24,12) Golay code. The hexacode-based Golay decoders can also accept hard inputs, and are less complex than other hard-decision Golay decoders. The drawback of the hexacode-based Golay decoders is that the Golay code must be represented in a very particular format. Encoding of information packets to be decoded with a hexacode-based Golay decoder is accomplished by a multi-level hexacode based Golay encoder, as described in a paper by O. Amrani, Y. Be'ery, A, Vardy, F. Sun, and H. van Tilborg entitled: "The Leech lattice and the Golay code: Bounded Distance Decoding and Multi-level Constructions", IEEE Trans. Inform. Theory, Vol. IT-40, pp. 1030-1043, July 1994. The multi-level Golay encoder is non-systematic, such that the input bits to the encoder do not appear within the output bits of the encoder. Non-systematic encoders cause a slightly worse decoded information bit error rate (BER) than systematic encoders due to error propagation.
Thus there is a need for a communication system that provides for a systematic encoder for the hexacode-based Golay decoders.